Overview
- Approaches integration and introductory analysis in a nonstandard way
- New edition expanded and extensively revised, including a new chapter on the Sunrise Lemma and applications
- Completely self-contained text
- Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (6 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
Involving rigorous analysis, computational dexterity, and a breadth of applications, this text is ideal for an undergraduate honors calculus course or for an introduction to analysis. This fourth edition includes corrections as well as some additional material.
Some features of the text:
• The text is completely self-contained and starts with the real number axioms;
• The integral is defined as the area under the graph, while the area is defined for every subset of the plane;
• There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero;
• There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more;
• Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals;
• self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma
• There are 450 problems with all the solutions at the back of the text.
Reviews from previous editions:
"This is a very intriguing, decidedly unusual, and very satisfying treatment of calculus and introductory analysis. It's full of quirky little approaches to standard topics that make one wonder over and over again, 'Why is it never done like this?'"
—John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper
"Chapter 5 is... an astonishing tour de force"
—Steven G. Krantz, The American Mathematical Monthly
"For a treatment [of infinite products and the Bernoulli series] that is very close to Euler’s and even more elementary..." — V.S. Varadarajan, Bulletin of the American Mathematical Society
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Introduction to Calculus and Classical Analysis
Authors: Omar Hijab
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-28400-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-28399-9Published: 17 February 2016
Softcover ISBN: 978-3-319-80345-6Published: 30 March 2018
eBook ISBN: 978-3-319-28400-2Published: 09 February 2016
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 4
Number of Pages: XIII, 427
Number of Illustrations: 1 b/w illustrations, 68 illustrations in colour
Topics: Approximations and Expansions, Sequences, Series, Summability, Special Functions, Combinatorics